Self-intersections in combinatorial topology: statistical structure (Q421024)
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scientific article; zbMATH DE number 6037983
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Self-intersections in combinatorial topology: statistical structure |
scientific article; zbMATH DE number 6037983 |
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Self-intersections in combinatorial topology: statistical structure (English)
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23 May 2012
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The authors provide statistical information on the number of self-intersections of randomly chosen oriented closed curves on a given closed orientable surface. Each such curve can be represented as a word with respect to a fixed set of generators of the fundamental group. The main result says that the distribution of the number of self-intersections of a closed oriented curve of fixed word length (uniformly chosen at random) is asymptotically Gaussian. The quite accessible proof employs U-statistics of a suitably crafted Markov chain.
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closed orientable surface
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random words in generators of fundamental group
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